{
  "id": "math/0010149",
  "version": "v1",
  "published": "2000-10-15T03:33:55.000Z",
  "updated": "2000-10-15T03:33:55.000Z",
  "title": "Generating Functions, Weighted and Non-Weighted Sums for Powers of Second-Order Recurrence Sequences",
  "authors": [
    "Pantelimon Stanica"
  ],
  "comment": "15 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper we find closed form for the generating function of powers of any non-degenerate second-order recurrence sequence, completing a study begun by Carlitz and Riordan in 1962. Moreover, we generalize a theorem of Horadam on partial sums involving such sequences. Also, we find closed forms for weighted (by binomial coefficients) partial sums of powers of any non-degenerate second-order recurrence sequences. As corollaries we give some known and seemingly unknown identities and derive some very interesting congruence relations involving Fibonacci and Lucas sequences.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-10-15T03:33:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A10",
      "05A19",
      "11B37",
      "11B39",
      "11B65"
    ],
    "keywords": [
      "generating function",
      "non-degenerate second-order recurrence sequence",
      "non-weighted sums",
      "partial sums",
      "closed form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math.....10149S"
    }
  }
}